{
  "abstract": "We study singular minimizing capillary cones with free boundary. We provide a stability criterion à la Jerison–Savin and use it to prove that a minimizing capillary cone is flat when its free boundary mean curvature is non-negative and $$n\\le 4$$ n ≤ 4 , or non-positive and $$n\\le 6$$ n ≤ 6 . We also show that minimizing cones with axially symmetric free boundary are flat in dimensions up to $$6$$ 6 , and derive improved regularity results for graphical minimizing capillary hypersurfaces. The proofs rely on Simons-type inequalities for convex, homogeneous, symmetric functions of the principal curvatures, coupled with a boundary identity intrinsic to the capillary setting.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, ETH Zurich, Ramistrasse 101, 8092, Zurich, Switzerland",
    "Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Via Carlo Alberto 10, 10124, Turin, Italy",
    "Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo, 5, 56127, Pisa, Italy"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Alberto Pacati",
      "orcid": "0009-0008-6744-1843"
    },
    {
      "affs": [
        1
      ],
      "name": "Giorgio Tortone",
      "orcid": "0000-0002-2728-3050"
    },
    {
      "affs": [
        2
      ],
      "name": "Bozhidar Velichkov",
      "orcid": "0000-0003-4968-3087"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4qs3g9fvvft2v.bib",
  "cited_by": 11,
  "doi": "10.1007/s12220-026-02616-5",
  "fulltext_url": null,
  "id": "4qs3g9fvvft2v",
  "issns": [
    "1050-6926",
    "1559-002X"
  ],
  "landing_url": "https://doi.org/10.1007/s12220-026-02616-5",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W4407425812",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/s12220-026-02616-5.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": "Springer Science+Business Media",
  "ris": "https://research.draconitic.com/paper/4qs3g9fvvft2v.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T13:20:42Z",
      "native_id": "W4407425812",
      "source": "openalex",
      "url": "https://doi.org/10.1007/s12220-026-02616-5"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Geometric Analysis and Curvature Flows",
      "subfield": "general"
    }
  ],
  "title": "Some Remarks on Singular Capillary Cones with Free Boundary",
  "title_text": "Some Remarks on Singular Capillary Cones with Free Boundary",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T13:20:42Z",
  "url": "https://research.draconitic.com/paper/4qs3g9fvvft2v",
  "venue": "Journal of Geometric Analysis",
  "versions": []
}